Businesses produce and sell a variety of products in different market structures at different price levels. To maximize their profit in the market, they have to take the costs of the production into account as well. To understand how the firms calculate the cost functions and derive their production plan, we should have a close look at two main cost types: and average cost. In this article, we will learn all about the average cost, its equation, and what the average cost function looks like with various examples. Ready to deep dive, let’s go!
Average Cost Definition
Average Cost, also called average total cost (ATC), is the cost per output unit. We can calculate the average cost by dividing the total cost (TC) by the total output quantity (Q).
Average Cost equals the per-unit cost of production, which is calculated by dividing the total cost by the total output.
Total cost means the sum of all costs, including fixed and variable costs. Therefore, average Cost is also often called the total cost per unit or the average total cost.
For example, if a company produces 1,000 widgets at a total cost of $10,000, the average cost per widget would be $10 ($10,000 ÷ 1,000 widgets). This means that on average, it costs the company $10 to produce each widget.
Average Cost Formula
The average cost is important for firms since it shows them how much each unit of output costs them.
Remember, it shows how much an additional unit of output costs the firm to produce.
\(\hbox{Average total cost} = \frac{\hbox{Total cost}}{\hbox{Quantity of output}}\)
We can calculate the average cost using the following equation, where TC stands for the total cost and Q means the total quantity.
The average cost formula is:
\(ATC = \frac{TC}{Q}\)
How can we calculate the average cost using the average cost formula?
Let's say the Generic Electronics company produces various gadgets. Their total costs and different levels of quantity are given in the following table. Using the average cost formula, we divide the total cost by the corresponding quantity for each level of quantity in the third column:
| Table 1. Calculating Average Cost | ||
|---|---|---|
| Total Cost ($) | Quantity of Output | Average Cost ($) |
| 500 | 50 | 10 |
| 900 | 100 | 9 |
| 1600 | 200 | 8 |
As we see in this example, we should divide the total cost by the quantity of output to find the average cost. For instance, for a total cost of $900, we can produce 100 gadgets. Therefore, the average cost for the production of 100 gadgets is $9. This demonstrates average cost decreasing as the fixed costs are spread between more output.
Components of the Average Cost Equation
The average total cost equation breaks into two components: average fixed cost, and average variable cost.
Average fixed cost formula
Average fixed cost (AFC) shows us the total fixed cost for each unit. To calculate the average fixed cost, we have to divide the total fixed cost by the total quantity:
\(\hbox{Average fixed cost}=\frac{\hbox{Fixed cost}}{\hbox{Quantity of output}}\)
\(AFC=\frac{FC}{Q}\)
Fixed costs are not connected to the quantity of produced output. Fixed costs the firms have to pay, even at a production level of 0. Let's say a firm has to spend $2000 a month for rent and it does not matter whether the firm is active that month or not. Thus, $2000, in this case, is a fixed cost.
Average variable cost formula
Average variable cost (AVC) equals the total variable cost per unit of produced quantity. Similarly, to calculate the average variable cost, we should divide the total variable cost by the total quantity:
\(\hbox{Average variable cost}=\frac{\hbox{Variable cost}}{\hbox{Quantity of output}}\)
\(AVC=\frac{VC}{Q}\)
Variable costs are production costs that differ depending on the total output of production.
A firm decides to produce 200 units. If raw materials cost $300 and labor to refine them costs $500.
$300+$500=$800 variable cost.
$800/200(units) =$4 Average Variable Cost.
The average cost is the sum of the fixed cost and average cost. Thus, if we add the average fixed cost and average variable cost, we should find the average total cost.
\(\hbox{Total average cost}=\hbox{Average variable cost (AVC)}+\hbox{Average fixed cost (AFC)}\)
The Average Fixed Cost and the Spreading Effect
The average fixed cost decreases with increasing produced quantity because the fixed cost is a fixed amount. This means it does not change with the produced amount of units.
When starting a bakery, the fixed cost is the initial investment required to open the business. This includes purchasing necessary equipment, stands, and tables. Essentially, fixed costs represent the upfront expenses needed to begin production.
As the total fixed cost remains constant, producing more units will lower the average fixed cost per unit. This is why the average fixed cost curve in Figure 1 slopes downwards.
This phenomenon is known as the spreading effect, where the fixed cost is spread out over the quantity produced. With a fixed amount of cost, the average fixed cost decreases as production increases.
Understanding Average Variable Cost and Diminishing Returns
In contrast, the average variable cost tends to rise. Each additional unit produced requires more variable input, leading to higher variable costs. This is referred to as the law of diminishing returns to variable input.
The rising average variable cost is a result of the diminishing returns effect. As output increases, more variable input is needed, causing higher average variable costs.
The U-shaped Average Total Cost Curve
How do the spreading effect and diminishing returns impact the shape of the Average Cost Function? The interplay between these two effects determines the U-shaped curve of the Average Cost Function.
Initially, the spreading effect outweighs the diminishing returns effect at lower output levels. Small increases in output lead to significant changes in average fixed cost.
For instance, if a firm starts with a fixed cost of $200, the average fixed cost for the first 2 units of production would be $100. As production reaches 4 units, the fixed cost halves to $50, showcasing the strong influence of the spreading effect at lower quantities.
At higher output levels, the average fixed cost is already distributed across the quantity produced, exerting minimal impact on the average total cost. Conversely, diminishing returns intensify as output rises, causing the diminishing returns effect to dominate over the spreading effect for larger quantities.
Illustrative Average Cost Scenarios
Understanding how to calculate the Average Cost using the total fixed cost and average variable cost is crucial. Let's practice calculating the Average Cost and explore the example of Generic Electronics, a company specializing in affordable consumer electronics. Everyone uses electronics, so this should be relatable!
In the table below, you will find columns for the quantity produced, total cost, average variable cost, average fixed cost, and average total cost.
| Table 2. Average Cost Example | ||||
|---|---|---|---|---|
|
Quantity (gadgets) |
Average fixed cost ($) |
Average variable cost ($) |
Total costs ($) |
Average total cost ($) |
|
1 |
100 |
50 |
150 |
150 |
|
5 |
20 |
55 |
295 |
59 |
|
10 |
10 |
60 |
610 |
61 |
|
20 |
5 |
65 |
1300 |
65 |
|
25 |
4 |
70 |
1750 |
70 |
As Generic Electronics produces more gadgets, the total costs increase as expected. The variable cost of 1 unit is $50, and the average variable cost rises with each additional unit of gadget. The fixed cost for 1 unit of gadget is $100, and the average fixed cost is $100. It's worth noting that average fixed costs decrease as the total quantity increases.
At a quantity level of 20, fixed costs have spread out across the total output ($5). While the average variable cost is on the rise ($65), it increases less than the average fixed cost decreases. This leads to a lower average total cost ($65). This quantity is the most efficient to produce, as the average total cost is minimized.
At a quantity level of 25, we can see that despite the average fixed cost ($4) being minimized, the variable cost ($70) has increased due to diminishing returns. This results in a higher average total cost ($70), indicating that the efficient production quantity is lower than 25.
What's surprising is that the average total cost initially decreases and then increases as the quantity rises. It's important to differentiate between total cost and average total cost, as the former always increases with more quantity. However, the average total cost function follows a U-shape, first decreasing and then increasing as quantity increases.
Average Cost Function
The average total cost function typically exhibits a U-shape, decreasing at lower output levels before increasing as output quantities grow. This U-shaped curve reflects the interplay between two critical economic effects: the spreading effect, where average fixed costs decrease with increasing output, and the diminishing returns effect, which causes average variable costs to rise as production expands. The U-shape of the average cost function is a direct result of these dynamics.
Average Cost and Cost Minimization
The average total cost reaches its lowest point at a specific output level, where the effects of diminishing returns and cost spreading are balanced. This optimal point, where the average total cost is minimized, is crucial in achieving cost efficiency. At this minimum-cost output, the average total cost curve intersects with the marginal cost curve, indicating that marginal cost equals average total cost. This intersection is not coincidental but a fundamental principle in economics, emphasizing the significance of the minimum-cost output in cost management strategies.
Average Cost Summary
To understand average cost, it's essential to recognize that it's derived by dividing the total cost by the total output, yielding a per-unit cost of production. This includes both average fixed cost (AFC), which indicates the fixed cost per unit, and average variable cost (AVC), which covers the variable cost per unit. Together, these form the average total cost. Characteristically, the average total cost curve is U-shaped, initially decreasing due to the spreading effect of fixed costs over more units, and later increasing as diminishing returns set in at higher production levels.